Nick Clegg has said the church and state should be separated, a view he has expressed before but one that is likely to gain fresh currency after David Cameron described Britain as a Christian country.

Clegg, an atheist, said he would like to see the disestablishment of the Church of England, which would lead to the Queen's removal as the head of the church.

"In the long run it would be better for the church and better for people of faith, and better for Anglicans, if the church and the state were over time to stand on their own two separate feet," the deputy prime minister said on his LBC radio phone-in show. He said he did not think this would happen overnight.

The monarch has been head of the Church of England since Henry VIII's split with Rome in 1534. The Queen holds the title of Defender of the Faith.

"We are a plural society with citizens with a range of perspectives and a largely non-religious society. To constantly claim otherwise fosters alienation and division in our society," they wrote in an open letter.

But Clegg said Britain's history, heritage and architecture were "infused by Christian values", and he was not sure why people were worked up about the comments.

"I'm not a practising man of faith but I don't have a problem to say we have an important Christian identity and heritage," he said. "That is not to say we are exclusively Christian, everyone is a Christian or indeed that we have one Christian denomination. There are almost as many Catholics as Anglicans in this country.

"We should remember one of the greatest Christian values is tolerance. We are open to people of other denominations and faiths and none, and that sense of fair play and tolerance is what makes our country very special."